Details

sample76.0ms

Algorithm

intervals

Results

19.0ms	181×	body	80	valid
17.0ms	31×	body	1280	valid
11.0ms	256×	pre	80	true
9.0ms	22×	body	640	valid
6.0ms	17×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
18	2002
17	1985
16	1722
15	1474
14	1236
13	995
12	795
11	669
10	582
9	467
8	348
7	290
6	209
5	124
4	69
3	50
2	33
1	20
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log` `associate-/r/` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Counts

2 → 102

Calls

2 calls:

30.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
154.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series148.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
85.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	2016
3	2016
2	1170
1	342
0	130

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite754.0ms

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub`
1×	`associate--r-`

Counts

4 → 417

Calls

4 calls:

463.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
23.0ms	(/ alpha (+ (+ alpha beta) 2.0))
201.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series325.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
76.0ms	(/ beta (+ (+ alpha beta) 2.0))
75.0ms	(/ alpha (+ (+ alpha beta) 2.0))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

429 → 429

Iterations

Iter	Nodes
done	2002
2	2002
1	995
0	406

prune5.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.4b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite619.0ms

Algorithm

rewrite-expression-head

Rules

280×	`*-un-lft-identity`
141×	`add-sqr-sqrt`
137×	`times-frac`
131×	`add-cube-cbrt`
126×	`prod-diff`
87×	`distribute-lft-out`
68×	`log-prod`
65×	`exp-sum`
21×	`fma-neg`
18×	`associate-/r/`
10×	`associate-/r*`
9×	`flip3-+` `flip-+` `div-inv`
8×	`add-cbrt-cube` `add-exp-log`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `div-exp` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 269

Calls

4 calls:

31.0ms	(/ beta (+ (+ alpha beta) 2.0))
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
371.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
166.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series418.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ beta (+ (+ alpha beta) 2.0))
88.0ms	(/ alpha (+ (+ alpha beta) 2.0))
110.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
136.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

281 → 281

Iterations

Iter	Nodes
done	2010
3	2010
2	1756
1	664
0	352

prune3.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize33.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
106×	`times-frac`
93×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
63×	`cbrt-prod` `prod-diff` `distribute-lft-out`
21×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 201

Calls

4 calls:

150.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
17.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
20.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
185.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
242.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
206.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.3s

Counts

213 → 213

Iterations

Iter	Nodes
done	2012
3	2012
2	1334
1	523
0	243

prune2.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

regimes223.0ms

Accuracy

99.2% (0.1b remaining)

Error of 3.1b against oracle of 3.0b and baseline of 15.5b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	29

end0.0ms

sample2.3s

Algorithm

intervals

Results

660.0ms	713×	body	640	valid
582.0ms	5880×	body	80	valid
357.0ms	8000×	pre	80	true
356.0ms	837×	body	1280	valid
87.0ms	371×	body	320	valid
31.0ms	199×	body	160	valid